1. Field of the Invention
This invention relates to a harmonic component measuring method for finding an admittance (impedance) and an equivalent circuit for a harmonic (measurement harmonic) in a power system.
2. Description of the Prior Art
To suppress harmonics in a power delivery and distributing system, importance has been attached to decreasing harmonics by a so-called system change technique using harmonic loss. The frequency of a harmonic produced by a system change is an integral multiple of the frequency of the fundamental wave of a system power supply, fs. For example, the frequency of the fifth harmonic, a representative harmonic, is 5*fs. To predict the voltage level of the harmonic, it is necessary to keep track of the harmonic characteristic upstream and downstream from the connection point of the filter in the power system and find its equivalent circuit. The equivalent circuit can be assumed to be a parallel circuit of an admittance element and a current source or a series circuit of an impedance element and a voltage source. The admittance or impedance is the most important to keep track of the harmonic characteristic.
It is described in Denkigakkai ronbunshi B, vol. 101 No. 8, p.451-p.458 (sho 56-8) that to find an equivalent circuit for the fifth harmonic of a power distribution line, the voltage and current of a fundamental wave in the system are measured. From the voltage and current measurements, the admittance (impedance) element and the current source (voltage source) size and phase of the harmonic equivalent circuit are calculated and estimated. However, the equivalent circuit cannot be accurately determined based on the voltage and current measurements of the fundamental wave as described in Denkigakkai.
For example, if an attempt is made to inject (apply) current (voltage) of a frequency which is an integral multiple of the fundamental wave (frequency fs), m*fs (m is an integer of 1, 2, . . . ), into the connection point of the filter and find an equivalent circuit to the harmonic from the measurement results of currents, voltages, etc., points in the system, since the harmonic exists in the power system, change in current, voltage, etc., based on the injected harmonic change cannot clearly be measured and the admittance (impedance) in the power system for the harmonic and an equivalent circuit to the harmonic cannot precisely be found. Therefore, the admittances (impedances) for the harmonics upstream and downstream from the connection point of the filter in the power system and equivalent circuits to the harmonics cannot be found separately with accuracy. Resultantly, a highly accurate prediction of the harmonic voltage level when the system is changed cannot be carried out.
By the way, assuming that the mth-degree harmonic is adopted as a measurement harmonic, currents or voltages of frequencies which are non-integral multiples of the fundamental wave above and below the measurement harmonic do not originally exist in a power system (actual system). Thus, an admittance for the measurement harmonic in the power system and an equivalent circuit to the measurement harmonic can be found from the measurement results based on injecting or applying the currents or voltages as follows:
Currents (voltages) of frequencies which are non-integral multiples of the fundamental wave above and below the measurement harmonic are injected into or applied to the power system and the admittances (impedances) above and below the measurement harmonic in the power system are found from the measurement results.
Interpolation processing such as averaging is applied to the admittances (impedances) above and below the measurement harmonic and the admittance (impedance) in the power system for the resultant intermediate measurement harmonic is found.
Further, when an equivalent circuit is found, a current source (voltage source) for the measurement harmonic in the power system is found from the found admittance (impedance) and the current (voltage) measurement result for the measurement harmonic in the power system and an equivalent circuit made of a parallel circuit of the admittance and the current source or a series circuit of the impedance and the voltage source is found.
In this case, the admittances (impedances) in the power system based on the currents (voltages) of frequencies which are non-integral multiples of the fundamental wave can be found precisely from the measurement results, thus the measurement harmonic admittance (impedance) and equivalent circuit can be found precisely.
However, since voltage or current measurements in the power system based on injecting or applying currents (voltages) of frequencies which are non-integral multiples of the fundamental wave is executed by processing the sampling result by carrying out a frequency analysis such as digital Fourier analysis (DFT), it is not easy to appropriately define the frequencies of the currents (voltages) of frequencies of non-integral multiples of the fundamental wave considering the measurement accuracy requirement, suppression of an analysis error caused by so-called sampling edges, and the like.
Particularly, to adopt a plurality of currents (voltages) of frequencies which are non-integral multiples of the fundamental wave each above and below the measurement harmonic and find the admittances (impedances) each above and below the measurement harmonic more accurately from measurement result averages, etc., it is extremely difficult to determine the frequency of the current (voltage) of the frequency of each non-integral multiple of the fundamental wave.
The analysis error caused by sampling edges is a frequency analysis error caused by discontinuity between the start and end of sampling. If the sampling frequency is made sufficiently higher than the fundamental wave frequency to prevent the error, a measuring apparatus becomes expensive and complicated.
Currents or voltages of frequencies which are non-integral multiples of the fundamental wave above and below the measurement harmonic may exist in an actual power system and the frequencies and magnitudes vary depending on the system, time period, etc.
If a current or voltage source has the same frequency as the current injected into or voltage applied to the power system, the measurement harmonic admittance (impedance) and the equivalent circuit cannot be found precisely. It is desirable to adopt a plurality of injected currents (applied voltages) of frequencies which are non-integral multiples of the fundamental wave each above and below the measurement harmonic and find an equivalent admittance (impedance) and an equivalent circuit to the measurement harmonic with the effect of the current source (voltage source) existing in the power system excluded as much as possible from an average of measurement results, etc., based on the injected currents (applied voltages).
However, if injected currents (applied voltages) of frequencies each above and below the measurement harmonic are injected (applied) one at a time and measurement is repeated, rapid measurement cannot be executed in a short time and moreover an error based on a measurement time lag easily occurs; an equivalent admittance (impedance) or an equivalent circuit cannot be found rapidly with accuracy.
If the frequencies of the injected currents (applied voltages) are only set, for example, in order starting at the frequency close to the measurement frequency, the effect of the current (voltage) existing in the power system cannot be minimized for measurement and highly accurate measurement with less injected current (applied voltage) cannot be accomplished.
Because of a restriction from the viewpoint of the power capacity, etc., of a unit for forming the injected currents (applied voltages), as the number of injected currents (applied voltages) is increased, the injected current amount (applied voltage) of each frequency decreases (lowers); particularly with a small unit of a small power capacity, when the harmonic in the power system is comparatively large, shortage of the injected current amount (applied voltage) occurs and measurement cannot be carried out depending on the number of injected currents, etc.
From the aspect of measurement accuracy, etc., it is desirable to increase the inject amount of the current of a frequency which is a non-integral multiple of the fundamental wave, but the load condition on the power system varies depending on the system, time period, etc., and it is extremely difficult to set the inject amount appropriately.
If a constant amount of current properly set is only injected into the power system for measurement, the degree of voltage distortion relative to the injected frequency into the power system changes with change in the load condition, thus shortage of the injected current amount occurs in some cases and measurement cannot be accomplished with intended accuracy.
Further, if the injected frequency matches or is close to a resonance point in the power system, the distortion voltage in the power system based on frequency injecting is enlarged remarkably due to resonance, thus it is feared that an excessive distortion voltage of a frequency which is a non-integral multiple of the fundamental wave may occur in the power system, adversely affecting load on the power system.
Since the load condition on the power system varies from moment to moment and is unknown and it is impossible to keep track of resonance frequency, it is impossible to inject an optimum amount of a current of a frequency which is a non integral multiple of the fundamental wave not adversely affecting the load on the power system and to precisely find the admittance or the equivalent circuit to the measurement harmonic from the measurement result.